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Self-similar Markov trees (based on a joint work in progress with Nicolas Curien and Armand Riera)

Vortrag von Prof. Dr. Jean Bertoin
Datum: 13.06.23   Zeit: 13.30 - 14.30   Raum: Y27H28

We represent a Galton-Watson process with types by a discrete genealogical tree with a decoration induced by the types of particles on each segment. When types are integers, such decorated trees can be re-normalized and we provide criteria for the existence of a scaling limit in terms of the reproduction laws of the Galton-Watson process. The limit is described as a self-similar Markov tree. The latter is a random real tree endowed with a decoration that records the evolution of types along branches, and a mass measure that accounts for the asymptotic repartition of particles.